Sam and Taylor own and operate a car wash service. Sam cleans the interior of each car and Taylor cleans the exterior. The time it takes Sam to finish the interior has a mean of 20 minutes with a standard deviation of 6.4 minutes. The time it takes Taylor to finish the exterior has a mean of 18 minutes with a standard deviation of 4.8 minutes. Both of their finishing times are approximately normally distributed.
Suppose we select a car at random, and define the random variable D as the difference between their finishing times. We can assume that their times are independent.
Find the probability that they finish within 10minutes of each other.
You may round your answer to two decimal places.
P\left(|D|<10\right)\approxP(∣D∣<10)≈P